How do you solve Find Nth Smallest Integer With K One Bits on LeetCode?

Find Nth Smallest Integer With K One Bits (LeetCode #3821) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Understanding binary representation is crucial.

What is the time complexity of Find Nth Smallest Integer With K One Bits?

The optimal solution for Find Nth Smallest Integer With K One Bits runs in O(n) time and uses O(n) space. The algorithm efficiently computes the result using combinatorial counting, leading to linear complexity in terms of n.

What is the brute force solution for Find Nth Smallest Integer With K One Bits?

The brute force approach for Find Nth Smallest Integer With K One Bits is Brute Force, with O(n²) time complexity and O(1) space complexity. Generate all integers and check their binary representation for exactly k ones. This method is straightforward but inefficient for large inputs. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find Nth Smallest Integer With K One Bits?

Find Nth Smallest Integer With K One Bits uses the following concepts: Math, Bit Manipulation, Combinatorics. The recommended patterns to study are: Combinatorics, Bit Manipulation.

What are the interview tips for Find Nth Smallest Integer With K One Bits?

Explain your thought process clearly. Practice combinatorial problems to build intuition. Think about edge cases and constraints.

What are common mistakes when solving Find Nth Smallest Integer With K One Bits?

Overlooking the need for combinatorial counting. Miscounting binary ones due to incorrect bit manipulation.

#3821

Find Nth Smallest Integer With K One Bits

Hard

MathBit ManipulationCombinatoricsCombinatoricsBit Manipulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

Use combinatorial mathematics to directly calculate the nth integer with k ones by determining how many valid integers exist for each bit length.

⚙️

Algorithm

3 steps

1Step 1: Precompute binomial coefficients C(i, k) for i from k to 50.
2Step 2: Iterate through bit lengths, using the coefficients to count how many integers with k ones fit within the current range.
3Step 3: Construct the nth integer by placing ones in the appropriate bit positions based on the counts.

solution.py15 lines

1from math import comb
2
3def nthSmallest(n, k):
4    result, bits = 0, 0
5    while True:
6        if comb(bits, k) >= n:
7            break
8        n -= comb(bits, k)
9        bits += 1
10    for i in range(bits, -1, -1):
11        if comb(i, k) >= n:
12            result |= 1 << i
13            n -= comb(i, k)
14            k -= 1
15    return result

ℹ

Complexity note: The algorithm efficiently computes the result using combinatorial counting, leading to linear complexity in terms of n.

1Understanding binary representation is crucial.
2Combinatorial counting helps in efficiently finding the nth integer.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.